.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "matplotlib/plot_animated_circ_billiard.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_matplotlib_plot_animated_circ_billiard.py: billiard trajectory in a circle (animated) ========================================== .. GENERATED FROM PYTHON SOURCE LINES 5-92 .. container:: sphx-glr-animation .. raw:: html

.. code-block:: default import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation from collections import deque def df(x): return np.array([2*x[0], 2*x[1]]) def intersection(vec0, coord): a = vec0[1]/vec0[0] if np.abs(a) > 1e7: z = np.array([x1, -y0]) x0 = coord[0] y0 = coord[1] sg = np.sign(vec0[0]) D = 1 - a**2*(-1+x0**2)+ 2*a*x0*y0 -y0**2 x1 = - ( -a**2*x0 + a*y0 - sg * np.sqrt(D) ) / (1 + a**2) y1 = (y0 -a * ( x0 - sg* np.sqrt(D) ) )/ (1 + a**2) z = np.array([x1, y1]) return z fig = plt.figure(figsize=(5, 5)) ax = fig.add_subplot(autoscale_on=False) ax.set_aspect('equal') ax.axis('off') theta = np.linspace(-np.pi, np.pi, 100) z = np.exp(1j*theta) ax.plot(z.real, z.imag, '-k',lw=3) ax.set_xlim(-1.1, 1.1) ax.set_ylim(-1.1, 1.1) point0, = ax.plot([], [], 'o') trace0, = ax.plot([], [], '-', lw=2, ms=2, c=point0.get_color()) dt = 0.2 history_len = 50 history_x0, history_y0 = deque(maxlen=history_len), deque(maxlen=history_len) x0 = np.array([0.1, 0.4]) vec0 = np.array([0.1, 0.02]) traj0 = [np.array([x0[0]]), np.array([x0[1]])] for i in range(300): x1 = x0 + vec0*dt if x1[0]**2 + x1[1]**2 > 1: x1 = intersection(vec0, x0) n = -df(x1) pn = -np.dot(vec0, n)/np.dot(n, n) * n vec0 = vec0 + 2*pn traj0[0] = np.append(traj0[0], x1[0]) traj0[1] = np.append(traj0[1], x1[1]) x0 = x1.copy() def animate(i): traj_x0,traj_y0 = traj0[0], traj0[1] thisx0 = traj_x0[i] thisy0 = traj_y0[i] if i == 0: history_x0.clear() history_y0.clear() history_x0.appendleft(thisx0) history_y0.appendleft(thisy0) point0.set_data(thisx0, thisy0) trace0.set_data(history_x0, history_y0) return point0, trace0 ani = animation.FuncAnimation( fig, animate, len(traj0[0]), interval=200*dt, blit=True) #, len(y1), interval=dt*1000, blit=True) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 7.123 seconds) .. _sphx_glr_download_matplotlib_plot_animated_circ_billiard.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_animated_circ_billiard.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_animated_circ_billiard.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_